Thresholdless dynamical instability in transverse $\mathcal{PT}$-symmetric scattering systems: The hidden role of bound states in the continuum

• URL: http://arxiv.org/abs/2608.29557v1
• Date: Sun, 30 Aug 2026 04:57:14 GMT
• Title: Thresholdless dynamical instability in transverse $\mathcal{PT}$-symmetric scattering systems: The hidden role of bound states in the continuum
• Abstract summary: We find a thresholdless dynamical instability in transverse parity-time ($mathcalPT$) symmetric systems.<n>The instability sets in at arbitrarily small $$ whenever $_V>0$.<n>These results establish a microscopic stability criterion and a design principle for stable $mathcalPT$-symmetric scattering devices.
• Score: 5.256849867954237
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The stationary scattering properties of transverse parity-time ($\mathcal{PT}$) symmetric systems have been extensively studied, yet their dynamical stability, a prerequisite for any stationary description, remains largely unexplored. Here we uncover a thresholdless dynamical instability in such systems, driven by symmetry-protected bound states in the continuum (BICs). Without gain and loss, the up-down mirror symmetry of the transverse geometry generically protects a BIC, which manifests as the coalescence of an $S$-matrix pole and zero on the real axis of the complex wave-number plane. A Hermitian symmetry-breaking perturbation shifts the poles into the lower half-plane, converting the BIC into a resonance with a Fermi-golden-rule decay width. An anti-Hermitian $\mathcal{PT}$-symmetric perturbation instead reverses the sign of the second-order energy shift, driving the poles into the upper half-plane and producing a time-growing bound state with $\operatorname{Im}E=γ^{2}Γ_{V}/2+O(γ^{3})$, where $γ$ is the gain-loss strength and $Γ_{V}$ is the golden-rule coupling of the BIC to the continuum. The instability therefore sets in at arbitrarily small $γ$ whenever $Γ_{V}>0$. We confirm this mechanism in a three-site side-coupled model that is unstable despite possessing a unitary scattering matrix, and in a four-site rhombic model where transverse and longitudinal gain-loss placements yield vanishing and finite thresholds, respectively. These results establish a microscopic stability criterion and a design principle for stable $\mathcal{PT}$-symmetric scattering devices.

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